The hydro power plant transforms one form of energy into another. However, the total amount of energy of the water stays the same until it enters the turbine.

Explain how this statement is supported by the three column charts above.

*attached is the column charts

The hydro power plant consists of a (artificial) dam that builds gravitational potential energy, P.E. from natural flowing water sources, by locating the dam along the water path. The stored potential energy, P. is converted into kinetic energy, K.E. as the water falls from the dam, down to the turbines, located at a much lower level according to the following principle of conservation of energy equation;

Total Mechanical Energy, M.E. = The potential energy of the water, P.E. + The kinetic energy of the water, K.E. = Constant

M.E. = P.E. + K.E. = Constant

Where;

P.E. = m·g·h

K.E. = (1/2)·m·v²

m = Mass

g = The acceleration due to gravity

h = The height of the dam

v = The velocity

The charts can be explained as follows;

Given that the potential energy P.E. = m·g·h, we have that the potential energy is directly proportional to the height of the dam, and therefore, at mid height, the potential energy would be half the maximum value, and we have;

At mid height, P.E. = (1/2)·

At the top of the dam, the (vertical) velocity of the water = 0, therefore, the kinetic energy = 0

Therefore, at the top of the dam, we get;

M.E. = + 0 =

M.E. =

Similarly, at the bottom of the dam, the height, h = 0, therefore, being proportional to the height, P.E. = 0, and the velocity is maximum, and at the bottom, we have;

M.E. = 0 +

The first chart, water is halfway down the dam

At the halfway down therefore, we have;

P.E. = (1/2)·

M.E. = = (1/2)·

∴ K.E. = - (1/2)·

Therefore the first chart, water is halfway down the dam;

Halfway, K.E. = (1/2)· = P.E.

∴ K.E. = P.E.  as shown on the chart

The second chart, water has reached the turbine

Water reaches the turbine at the bottom, and as explained above, we get;

M.E. = 0 +

∴ M.E.≈

Therefore, when water has reached the turbine at the bottom of the dam, the kinetic energy is approximately proportional to the total mechanical energy as shown in the chart

The third chart, water is at the top of the dam

Here as shown above, we have;

The total mechanical energy, M.E. ≈ as shown on the chart

Learn more about potential and kinetic energy here;